Simplify square root of 52

Problem

√(,52)

Solution

1. Identify the largest perfect square factor of the radicand 52

2. Factor the number 52 into a product of a perfect square and another integer.

√(,52)=√(,4⋅13)

3. Apply the product property of square roots, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,4⋅13)=√(,4)⋅√(,13)

4. Simplify the square root of the perfect square 4

√(,4)⋅√(,13)=2√(,13)

Final Answer

√(,52)=2√(,13)

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